Comparison of estimators of a dispersion matrix under generalized pitman nearness criterion

Abstract

Some equivariant estimators of the dispersion matrix of a multivariate normal population are compared using the generalized Pitman nearness criterion based on the entropy loss function. It is shown that, under the group of lower triangular transformations, a best equivariant estimator does not exist. Existence of best estimators in certain subclasses are discussed and the performances of two commonly used estimators are compared. Some properties of central chi-square distributions are obtained and used to derive the main results.

Keywords:

• admissibility
• entropy loss
• equivariant estimator
• median
• lower triangular transformation
• skewness
• transitive parameter space
• Wishart matrix